At the root of the left–right asymmetries in spatial–numerical processing: From domestic chicks to human subjects

The roles of motion, gesture, and embodied action in the processing of mathematical concepts

This article discusses perspective and frame of reference in the metaphorical description of mathematical concepts in terms of motions, gestures, and embodied actions. When a mathematical concept is described metaphorically in terms of gestures, embodied actions, or fictive motions, the motor system comes into play to ground and understand that concept. Every motion, gesture, or embodied action involves a perspective and a frame of reference. The flexibility in taking perspective and frame of reference allows people to embody a mathematical concept or idea in various ways. Based on the findings of past studies, it is suggested that the graphical representation of a mathematical concept may activate those areas of the motor system that are involved in the production of that graphical representation. This is supported by studies showing that when observers look at a painting or handwritten letters, they simulate the painter's or writer's hand movements during painting or writing. Likewise, the motor system can contribute to the grounding of abstract mathematical concepts, such as functions, numbers, and arithmetic operations.

Spatial-numerical associations from a novel paradigm support the mental number line account

Multiple tasks have been used to demonstrate the relation between numbers and space. The classic interpretation of these directional spatial-numerical associations (d-SNAs) is that they are the product of a mental number line (MNL), in which numerical magnitude is intrinsically associated with spatial position. The alternative account is that d-SNAs reflect task demands, such as explicit numerical judgements and/or categorical responses. In the novel "Where was The Number?" task, no explicit numerical judgements were made. Participants were simply required to reproduce the location of a numeral within a rectangular space. Using a between-subject design, we found that numbers, but not letters, biased participants' responses along the horizontal dimension, such that larger numbers were placed more rightward than smaller numbers, even when participants completed a concurrent verbal working memory task. These findings are consistent with the MNL account, such that numbers specifically are inherently left-to-right oriented in Western participants.

Spatial biases in mental arithmetic are independent of reading/writing habits: Evidence from French and Arabic speakers

The representation of numbers in human adults is linked to space. In Western cultures, small and large numbers are associated respectively with the left and right sides of space. An influential framework attributes the emergence of these spatial-numerical associations (SNAs) to cultural factors such as the direction of reading and writing, because SNAs were found to be reduced or inverted in right-to-left readers/writers (e.g., Arabic, Farsi, or Hebrew speakers). However, recent cross-cultural and animal studies cast doubt on the determining role of reading and writing directions on SNAs. In this study, we assessed this role in mental arithmetic, which requires explicit number manipulations and has revealed robust leftward or rightward biases in Western participants. We used a temporal order judgement task in French and Arabic speakers, two languages that have opposite reading/writing directions. Participants had to solve subtraction and addition problems presented auditorily while at the same time determining which of a left or right visual target appeared first on a screen. The results showed that the right target was favoured more often when solving additions than when solving subtractions both in the French- (n = 31) and Arabic-speaking (n = 25) groups. This was true even in Arabic-speaking participants whose preference for ordering of various series of numerical and non-numerical stimuli went from right to left (n = 10). These results indicate that SNAs in mental arithmetic cannot be explained by the direction of reading/writing habits and call for a reconsideration of current models to acknowledge the pervasive role of biological factors in SNAs in adults.

The ontogeny of continuous quantity discrimination in zebrafish larvae (Danio rerio)

Several studies have investigated the ontogeny of the capacity to discriminate between discrete numerical information in human and non-human animals. Contrarily, less attention has been devoted to the development of the capacity to discriminate continuous quantities. Recently, we set up a fast procedure for screening continuous quantity abilities in adult individuals of an animal model in neurodevelopmental research, the zebrafish. Two different sized holes are presented in a wall that divides the home tank in two halves and the spontaneous preference of fish for passing through the larger hole is exploited to measure their discrimination ability. We tested zebrafish larvae in the first, second and third week of life varying the relative size of the smaller circle (0.60, 0.75, 0.86, 0.91 area ratio). We found that the number of passages increased across the age. The capacity to discriminate the larger hole decreased as the ratio between the areas increased. No difference in accuracy was found as a function of age. The accuracy of larval zebrafish almost overlaps that found in adults in a previous study, suggesting a limited role of maturation and experience on the ability to estimate areas in this species.

Number-space associations without language: Evidence from preverbal human infants and non-human animal species

It is well known that humans describe and think of numbers as being represented in a spatial configuration, known as the 'mental number line'. The orientation of this representation appears to depend on the direction of writing and reading habits present in a given culture (e.g., left-to-right oriented in Western cultures), which makes this factor an ideal candidate to account for the origins of the spatial representation of numbers. However, a growing number of studies have demonstrated that non-verbal subjects (preverbal infants and non-human animals) spontaneously associate numbers and space. In this review, we discuss evidence showing that pre-verbal infants and non-human animals associate small numerical magnitudes with short spatial extents and left-sided space, and large numerical magnitudes with long spatial extents and right-sided space. Together this evidence supports the idea that a more biologically oriented view can account for the origins of the 'mental number line'. In this paper, we discuss this alternative view and elaborate on how culture can shape a core, fundamental, number-space association.

Anticlockwise or clockwise? A dynamic Perception-Action-Laterality model for directionality bias in visuospatial functioning

Orientation bias and directionality bias are two fundamental functional characteristics of the visual system. Reviewing the relevant literature in visual psychophysics and visual neuroscience we propose here a three-stage model of directionality bias in visuospatial functioning. We call this model the 'Perception-Action-Laterality' (PAL) hypothesis. We analyzed the research findings for a wide range of visuospatial tasks, showing that there are two major directionality trends in perceptual preference: clockwise versus anticlockwise. It appears these preferences are combinatorial, such that a majority of people fall in the first category demonstrating a preference for stimuli/objects arranged from left-to-right rather than from right-to-left, while people in the second category show an opposite trend. These perceptual biases can guide sensorimotor integration and action, creating two corresponding turner groups in the population. In support of PAL, we propose another model explaining the origins of the biases - how the neurogenetic factors and the cultural factors interact in a biased competition framework to determine the direction and extent of biases. This dynamic model can explain not only the two major categories of biases in terms of direction and strength, but also the unbiased, unreliably biased or mildly biased cases in visuosptial functioning.

Mapping number to space in the two hemispheres of the avian brain

Pre-verbal infants and non-human animals associate small numbers with the left space and large numbers with the right space. Birds and primates, trained to identify a given position in a sagittal series of identical positions, whenever required to respond on a left/right oriented series, referred the given position starting from the left end. Here, we extended this evidence by selectively investigating the role of either cerebral hemisphere, using the temporary monocular occlusion technique. In birds, lacking the corpus callosum, visual input is fed mainly to the contralateral hemisphere. We trained 4-day-old chicks to identify the 4th element in a sagittal series of 10 identical elements. At test, the series was identical but left/right oriented. Test was conducted in right monocular, left monocular or binocular condition of vision. Right monocular chicks pecked at the 4th right element; left monocular and binocular chicks pecked at the 4th left element. Data on monocular chicks demonstrate that both hemispheres deal with an ordinal (sequential) task. Data on binocular chicks indicate that the left bias is linked to a right hemisphere dominance, that allocates the attention toward the left hemispace. This constitutes a first step towards understanding the neural basis of number space mapping.